BURR CRITICAL VALUE APPROXIMATIONS FOR TESTS OF AUTOCORRELATION AND HETEROSCEDASTICITY

The paper evaluates the accuracy of Burr approximations of critical values and p-values for test a of autocorrelation and heteroscedasticity in the linear regression model.     

Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ Method

Utilizing time series modeling entails estimating the model parameters and dispersion. Classical estimators for autocorrelated observations are sensitive to presence of different types of outliers and lead to bias estimation and misinterpretation. It is important to present robust methods for parameters estimation which are not influenced by contaminations. In this article, an estimation method entitled Iteratively Robust Filtered Fast? τ(IRFFT) is proposed for general autoregressive models. In comparison to other commonly accepted methods, this method is more efficient and has lower sensitivity to contaminations due to having desirable robustness properties. This has been demonstrated by applying MSE, influence function, and breakdown point criteria.     

Influence measures in blocked designs of experiments with correlated errors

Diagnostics measures for detecting outliers in data from block designs of experiments with correlated errors are considered. Influence is often assessed by deleting suspected outlying observations. Autocorrelation of order one is considered to model correlation in each block. Cook-statistic is developed for detecting the effect of a single outlier, where results are illustrated with an example.     

Comparative Study of Generalized Estimating Equations and Logistic Regressions on Different Sample Sizes and Correlation Levels

In this study, it was aimed to determine accuracy of generalized estimating equations versus logistic regressions on different correlation levels and sample sizes. For this aim, two methods were compared with different sample sizes 10, 25, 50 and 100 and correlation levels 0.0, 0.3, 0.5 and 0.8. Result of this study showed that using generalized estimating equations could be preferred versus logistic regression when the sample size is over than 25 and correlation level is higher than 0.3 on data taken from studies with repeated measurements, but logistic regression could be better when the autocorrelations do not exist.     

A variable-neighbourhood search algorithm for finding optimal run orders in the presence of serial correlation

The responses obtained from response surface designs that are run sequentially often exhibit serial correlation or time trends. The order in which the runs of the design are performed then has an impact on the precision of the parameter estimators. This article proposes the use of a variable-neighbourhood search algorithm to compute run orders that guarantee a precise estimation of the effects of the experimental factors. The importance of using good run orders is demonstrated by seeking D-optimal run orders for a central composite design in the presence of an AR(1) autocorrelation pattern.     

Balanced and partially balanced incomplete block designs with autocorrelation errors

The paper aims to find variance balanced and variance partially balanced incomplete block designs when observations within blocks are autocorrelated and we call them BIBAC and PBIBAC designs. Orthogonal arrays of type I and type II when used as BIBAC designs have smaller average variance of elementary contrasts of treatment effects compared to the corresponding Balanced Incomplete Block (BIB) designs with homoscedastic, uncorrelated errors. The relative efficiency of BIB designs compared to BIBAC designs depends on the block size k and the autocorrelation ρ and is independent of the number of treatments. Further this relative efficiency increases with increasing k. Partially balanced incomplete block designs with autocorrelated errors are introduced using partially balanced incomplete block designs and orthogonal arrays of type I and type II.     

A simple recursive estimation method for linear regression models with AR(p) disturbances

An exact transformation that reduces the AR(p) process into white noise is well known in statistics, see Fuller (1976). However, practitioners still use and econometric textbooks still recommend the Cochrane-Orcutt procedure for p>2, see Greene (1990). This paper derives an alternative exact transformation for the AR(p) process which is computationally simple. Based on this transformation, a GLS estimator is proposed, requiring only least squares regressions and recursive computations. This is illustrated for the AR(3) case.     

Tests of serial independence based on Kendall's process

The authors propose new rank statistics for testing the white noise hypothesis in a time series. These statistics are Cramér‐von Mises and Kolmogorov‐Smirnov functionals of an empirical distribution function whose mean is related to a serial version of Kendall's tau through a linear transform. The authors determine the asymptotic behaviour of the underlying serial process and the large‐sample distribution of the proposed statistics under the null hypothesis of white noise. They also present simulation results showing the power of their tests.     

On Kendall's Autocorrelations

This brief article extends the theory of sample Kendall's autocorrelations by providing their exact variances at lags higher than one under the null hypothesis of randomness, by introducing and investigating their weighted modifications, and by numerical demonstration of these results and their usefulness.